WASHINGTON — Trade ministers for the United States and 11 other Pacific nations gathered in Atlanta on Wednesday to try to reach agreement on the largest regional free-trade pact ever. But knotty differences persist, and antitrade blasts from American presidential candidates have not eased prospects for any deal.

The talks in a downtown Atlanta hotel are picking up where ministers left off two months ago after deadlocking at a Maui resort, at odds over trade in pharmaceutical drugs, autos, sugar and dairy goods, among other matters. United States negotiators said last week that enough progress had been made in recent contacts to justify hosting another, perhaps final round.

For President Obama, who cited the potential agreement during his address this week to the United Nations, success in a negotiating effort as old as his administration would be a legacy achievement. The proposed Trans-Pacific Partnership would liberalize trade and open markets among a dozen nations on both sides of the Pacific, from Canada to Chile and Japan to Australia, that account for about two-fifths of the world’s economic output.

Failure would be just as big a defeat for Mr. Obama, and upset his long-troubled foreign policy initiative to reorient American engagement toward fast-growing Asia and away from the violent morass of the Middle East and North Africa. Yet if the Atlanta talks yield no agreement by the weekend, the Americans are unlikely to declare failure.

Time is not the president’s friend, however. Even if agreement is reached this week, Congress will not debate and vote on it until late winter — in the heat of the states’ presidential nominating contests — because by law Mr. Obama cannot sign the deal without giving lawmakers 90 days’ notice.

He will need bipartisan support, given the resistance of many Democrats and union allies to such trade accords. But presidential candidates in both parties have already registered strong opposition.

The Republican front-runner, Donald J. Trump, the billionaire who boasts of his own deal-making prowess, has called the emerging trans-Pacific agreement “a disaster.” While some Republican rivals also are critical, it is the rhetoric of Mr. Trump, given his celebrity appeal, that has Republican leaders more worried that a toxic trade debate could threaten vulnerable Republicans in 2016. Senator Mitch McConnell of Kentucky, the majority leader, supports a Pacific accord but nonetheless wants to protect his narrow Republican majority — and deny Mr. Obama an achievement.

On the Democratic side, where unions, progressive groups and many members of Congress oppose an agreement, Hillary Rodham Clinton has not taken a stand, though she repeatedly promoted the Pacific accord as secretary of state. In June, Mrs. Clinton told an Iowa audience “there should be no deal” if congressional Democrats’ concerns for workers were not addressed, and many in the party, including administration officials, expect she ultimately would oppose a deal, like her rival, Senator Bernie Sanders of Vermont.

The United States trade representative, Michael B. Froman, said before heading to Atlanta, “The president has made clear that he will only accept a T.P.P. agreement that delivers for middle-class families, supports American jobs and furthers our national security.”

“The substance of the negotiations will drive the timeline for completion,” Mr. Froman added, “not the other way around.”

Mr. Obama and Vice President Joseph R. Biden Jr., who has not ruled out a bid for president, showed at the United Nations that they were pressing hard to get an agreement. The president affirmed his support in private meetings with several world leaders, according to administration officials.

In his address to the United Nations, Mr. Obama told foreign leaders the accord would be a model for the world, “an agreement that will open markets, while protecting the rights of workers and protecting the environment that enables development to be sustained.” Should a deal come together, central to the White House campaign to sell the agreement to Congress would be the argument that setting economic, labor and environmental standards in the Pacific region would counter China’s influence, officials said.

Late Tuesday, Mr. Biden brought Mr. Froman to a Manhattan meeting with Prime Minister Shinzo Abe of Japan, who has made an agreement central to his own economic platform.

The Obama administration has pressed for the Pacific accord for six years, picking up the idea from the George W. Bush administration. Many issues have been all but settled, but nothing is final until everything is decided.

That progress, including tentative agreements on ending tariffs, setting labor and environmental standards, and opening certain markets, has sustained the negotiations despite setbacks.

But several issues continue to block a deal.

Dairy market rules divide the United States, Canada, Australia and New Zealand; this has been especially troublesome for Canada’s team, since the nation will hold elections this month.

Also divisive are provisions over auto exports, including requirements that autos have a certain percentage of parts made in countries that are parties to the agreement. Japan has sought a lower percentage of parts in the “rules of origin,” with some support from Americans, to allow the export of autos with Chinese parts, while Mexico and Canada demand stricter rules.

Perhaps most contentious are negotiations related to protections for pharmaceutical companies’ drugs, especially cutting-edge biologics that are made from living organisms and considered promising against cancer, among other ailments.

Several countries, especially Australia, have opposed the United States and its pharmaceutical industry for insisting that companies’ drug data be protected for 12 years to create financial incentives to innovate. Critics say this keeps lower-cost generic drugs and “biosimilars” off the market for too long.

Here, too, the presidential contest has injected a wild card: Mrs. Clinton and Mr. Sanders each have accused drug makers of price gouging.

While there is talk of an eight-year compromise, for many opponents that is too long. Judit Rius Sanjuan, a manager of a campaign by Doctors Without Borders to hasten access to lower-priced drugs and vaccines, said she met with American negotiators last week in Washington, “and they gave me zero indication that they are going to be more flexible on this issue.”

Andrew Spiegel, executive director of the Global Colon Cancer Association, said drug makers needed the incentives of strong protections for their intellectual property to encourage their research. He did not offer an answer to the question dividing negotiators: how many years the drug makers’ data monopoly should last.

“I leave it to them to pick the magic number,” Mr. Spiegel said.

Last week, 156 members of Congress, mostly Democrats, wrote the administration to complain that some parties to the talks, like Vietnam, Singapore and Japan, manipulate their currency values to underprice their products. While discussions are continuing, the administration is counting on reaching a currency deal with the Asian nations that would be a side agreement to any trade pact.